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842                           Appendix II.

tubes, for it is seen how /0 follows from p-^ and so on, but for
shrinkage a further value is given for clearness, thus :

q       f Shrinkage between 1
b4= ]         c and D         J -

The radii are first assumed, varying approximately in geo-
metrical progression outwardly. A limit is next placed on the
hoop tensions, and p% found. From /2 we pass to p and thence
PQ (the safe gas pressure) is deduced. Finally, the shrinkages are
calculated to give these pressures. A rough shrinkage rule is
given on p. 400.

v P. 400. Shrink Fits.  There are three methods of fitting                I

a   cylinder rigidly in  a  socket,  viz.   by driving, forcing,  and                 |
shrinking.    In all three, the cylinder must be larger than the

socket by an amount determined by experience.    The * largeness '                 |

for  driving  and force fits is given on p. 826; and for shrink                 }

fits, where the outer portion is heated before slipping over the                 t

cylinder, the following simple rules may be adopted :                            t

S = '0025 x diameter of hole                                            /

if the parts are very thick and unresisting ; but                                            I

S = '0035 x diameter of hole                                            \

if thinner and more elastic. Care must be taken not to heat
higher than is absolutely necessary, and to prevent endlong sliding
by means of clamps. (Seep. 825.)

^ P. 402. Strength of Bolts.  Engineers have disagreed
considerably as to the stress which comes on fluid-tight covers,
though the problem is easily determined. First, suppose the
flange and seating be quite rigid, and no packing be placed
between the surfaces; also that the necessary tightness is obtained
by an initial ' sere wing-up ' stress in the bolt, as at A, Fig. 807.
If now the fluid stress be exerted, the flange wiH tend to take the
condition B, but as it is evident that (the flanges being rigid) the
surfaces cannot separate till the pressure exceeds the initial stress,
it follows that the bolt cannot stretch till such stress is exceeded ;
and the bolt stress must either be that due to screwing or to